The combination of mesh adaptivity and aggregation constraints is not straightforward. First, the definition of ill-posed versus well-posed degrees of freedom is more complex. A degree of freedom that only belongs to cut elements can be well-posed because it constrains well-posed hanging degrees of freedom. The right intertwining of these two sets of constraints has been analyzed in [1]}. This work proposed a two-step algorithm to construct the discrete extension operator that carefully mixes aggregation constraints of problematic degrees of freedom and standard hanging degree of freedom constraints. Following this approach, the aggregated finite element space is defined as a discrete extension with well-defined linear constraints.
